Embodiment being a killer feature for AGI seems weird to me. Not only is "what is a body" vague, but it is entirely possible to build a body. So why would it prevent AGI?
We do know that embodiment is a sufficient condition for general intelligence: if we assume humans have general intelligence then it is clearly a sufficient condition. But the question of necessary is more interesting because we have to actually ask what embodiment means.
Is a computer a embodied machine? What about a robot that can explore its environment? What about a simulation with an environment? If no, what makes us distinct? If yes, does embodiment even matter?
To me it is clear that feature space is the more important issue. It is also clear that embodiment helps with creating a more complex and rich feature space. The ability to move around and interact with your environment greatly expands the complexity of the environment.
I think the bigger question is about our ability to create rich enough environments to generate intelligence. Even if we can get machines in bodies, can we get them into the complex and evolving environmental pressures that we experienced over millions of years (without robots living for similar timescales)? It is reasonable to think that at some point in time we'd be able to have that kind of computational power. It is also possible that the learning function is incredibly difficult. With a large and complex feature space there are many local extrema and it may be possible that general intelligence is only possible with a few of these (essentially we can have an estimation similar to the Drake Equation). But overall, I'm not sure there really is any issue that means AGI is impossible. Maybe at current knowledge and computational limits, maybe for all of the foreseeable future! But I don't see any limitations in physics that are killers.